Elastic anomalies in intermediate valence rare-earth intermetallics

Abstract The bulk moduli c B of Rare earth (R) and Actinide (A) intermetallics (R-Cu 2 Si 2 , R-Rh 2 , R-Ru 2 , R-Be 13 , A-Be 13 have been determined by means of Brillouin scattering. A softening of c B is found in EuCu 2 Si 2 , YbCu 2 Si 2 , CeCu 2 Si 2 and CeRh 2 , but not in UBe 13 . CeRu 2 shows a c B twice as large as that of LaRu 2 .

By means of an improved technique for Brillouin scattering, using a 3 + 3 pass tandem Fabry-Perot interferometer according to Sandercock [l], it has now become feasible to reliably measure bulk transverse and longitudinal acoustic sound velocities of metals. Thus we are able to determine the bulk modulus of both single crystals and polycrystals [2].
With the help of this method we have determined the bulk moduli ca of various polycrystalline Rare earth (R) and Actinide (A) intermetallics (R-Cu,Si,, R-Ru,, R-Rh,, R-and A-Be,,) with particular emphasis on intermediate valence effects. These should show up most pronounced in the bulk modulus because of the volume changes associated with 4f" c) 4f"-' + e-valence fluctuations. All measurements were carried out at room temperature. The cn values of each series of compounds (except R-Ru,) have been plotted as functions of Q/l', where Q is the valence of the R or A ion and V is the unit cell volume. 4f"-' + em configurational mixing near the Fermi level [3-51 which causes the R ions, and thus in turn the lattice, to become more compressible.
A comparison of our ca values with those determined by X-ray diffraction under hydrostatic pressure [6-81 as given elsewhere [2] shows good agreement within the error bars.
The 14% softening of cB of CeCu,Si z may also be associated with a valence instability effect, but even more so it may be indicative of the electron-phonon coupling in this " heavy-fermion" superconductor (T, = 0.5 K [9]). The large volume dependence of the spinfluctuation or Kondo temperature (T* = 10 K [9]) has recently been considered as the dominant electron-phonon coupling mechanism in CeCuzSi, [lo]. The softening of ca is consistent with such a Kondo volume collapse-type of electron-phonon interaction. An extraordinary situation is found in the case of the superconductor CeRu, (7; = 6.2 K [ll]). It turns out that ca of CeRu, is twice as large as that of the reference compound LaRu, (CeRu,: ca = 134 GPa, LaRu,: ca = 63 GPa). An explanation for this behavior can be found in the valence of CeRu,, which was determined by L,,, X-ray absorption as v = 3 + Y = 3.3 [12]. On the basis of this valence and the superconducting properties of CeRu, the Ce ion may be considered as in the a'-Ce type phase [13], where the valence is not pressure-dependent (dv/dp = 0). Thus in eq. 1 (1) the second term vanishes and therefore CeRu, should show at least no softening in cB, because the first term represents the "isovalent" contribution to the compressibility. Moreover, in the a'-phase of Ce the valence becomes reduced as compared to the a-phase of Ce [ 131, implying an increased volume of the Ce atom. Consequently, the a'-Ce type ion in CeRu, acquires a larger volume as compared to an a-Ce type ion. On the other hand, the unit cell volume of CeRu, is 6% smaller with respect to LaRu, (LaRu,: V = 457 A3, CeRu,: V= 428 A3 [14]). As a consequence of the "external" and the very large "internal" pressure the bulk modulus of CeRu, exceeds that of LaRu, by a factor of two.
CeRh, has a valence of 3.24 [12], which raises the I' question whether it is a-Ce or a'-Ce like [13] and might exhibit a similar behavior as CeRu,. The bulk modulus of CeRh, has been determined together with that of La-, Y-and LuRh,.
The cB vs. Q/V plot in fig. 2 shows a 20% softening of ca of CeRh, with respect to the reference line of the stable valent R-Rh,.
Hence we conclude that the behavior of CeRh, resembles that of the cu-Ce phase where the valence increases with increasing external pressure [13], so that the softening of cB is caused by the second term in eq. 1.
The series of R-and A-Be,, intermetallics has been investigated in order to clarify whether cB of intermediate valent CeBe,, is indeed larger than that of LuBei [15] and to determine cB of the supposed p-wave superconductor UBe,, [16] (T, = 0.85 K [17]). The results of CB vs. Q/V are shown in fig. 3. The overall magnitude of the cB values in fig. 3 is of the order of cB = 100 GPa of Be. This is due to the fact that the Be atoms form cages around the R or A ions and in first order dominate the elastic behavior. For the presently available data a tentative reference line has been indicated in fig. 3 by the dashed line. The scaling between R-and A-Be,, compounds has to be taken with some caution as seen by the behavior of their (q = 0) optical phonon frequencies tr w_,, vs. the Ce dilution in the Be matrix [l&19], a magnetoelastic coupling of the volume strain to two distinct electronic states (possibly reminiscent of I',-rs crystalline electric field excitations) has been used to explain the minimum in the temperature dependence of cn near 135 K [20].
The " heavy-fermion" superconductor UBe,, shows no anomaly in cu, even when assuming a horizontal reference line for the A-Be,,.
This result is in contrast to the behavior of CeCuzSi, and may be indicative of an electronic superconducting transition of UBe,, due to an interaction different from the usual electron-phonon interaction [16].